LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


GIFT  OK 


Co.... 

Class 


QUESTIONS  AND  EXERCISES 


TO  BE  USED  IN  CONNECTION  WITH 


OUTLINES  OF  PHYSICS 


AN  ELEMENTARY  TEXT-BOOK 


BY 

EDWARD   L.   NICHOLS 

PROFESSOR   OF   PHYSICS   IN   CORNELL   UNIVERSITY 


gorfe 
THE   MACMILLAN    COMPANY 

LONDON:  MACMILLAN  &  CO.,  LTD. 

1897 


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UNIVERSITY  OF  CALIFORNIA. 

GIFT  OF 
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Received  ..^Jpz-  ^t-  z-C^  /^^^) • 

Accession  No.*7t7<T2  3     .    Class  No. 

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• 


QUESTIONS  AND  EXERCISES 


TO  BE  USED  IN  CONNECTION  WITH 


OUTLINES  OF  PHYSICS 


AN  ELEMENTARY  TEXT-BOOK 


BY 

EDWARD   L.   NICHOLS 

PROFESSOR   OF   PHYSICS   IN   CORNELL   UNIVERSITY 


UJvU. 


THE   MACMILLAN    COMPANY 

LONDON:  MACMILLAN  &  CO.,  LTD. 

1897 

All  rights  reserved 


>PTEIGHT, 

BY  THE  MACMILLAN  COMPANY. 


NorfoooB 
J.  S.  Gushing  &  Co.  -  Berwick  ft  Smith 
Norwood  Mass.  U.S.A. 


A  SET  OF  QUESTIONS  AND  EXERCISES  TO  BE  USED  IN 
CONNECTION  WITH  NICHOLS'  OUTLINES  OF  PHYSICS 


CHAPTER  I 

1.  What  advantage  is  gained  by  expressing  fractions  of  a 
unit  (of  length,  mass,  or  time)  decimally  instead  of  by  means 
of  a  common  fraction  ? 

2.  What  is  the  mass,  expressed  in  grams,  of  1  cubic  meter 
of  water  ? 

3.  What  is  the  mass  (in  grams)  of  a  liter  of  water  ? 

4.  A    how  much   longer   distance  is  100  meters  than  100 
yards  ?     (Express  your  answer  (1)  in  meters,  (2)  in  centime- 
ters, (3)  in  yards.) 

5.  If  cloth  were  sold  by  the  meter  and  the  price  per  meter 
were  the  same  as  the  price  per  yard,  what  would  be  the  per- 
centage of  gain  to  the  buyer  ? 

6.  The  cyclometer  of  a  bicycle  records  1  mile  for  every  720 
revolutions  of  the  wheel.     li  it  is  to  record  kilometers,  once  in 
how  many  revolutions  of  the  wheel  must  it  be  made  to  record  ? 
(Solve  first  by  use  of  the  approximate  value  of  the  mile  given 
on  p.  4.     Then  compute  by  use  of  Appendix  I  and  find  the 
error,  in  revolutions  of  the  wheel,  introduced  by  taking  the 
approximate  ratio.) 

7.  If  in  Fig.  4  (p.  6)  the  line  ab  be  set  to  coincide  with 
scale  division  4,  what  will  be  the  position  of  cd  upon  the  scale  ? 


2  MECHANICS 

Is  there  anything  to  be  gained  by  thus  setting  one  of  the  lines 
to  coincide  with  a  scale  division  ? 

8.  In  Fig.  5  (p.  8)  suppose  the  tine  lines  of  the  cross-section 
paper  to  be  strictly  equidistant.     How  many  times  more  accu- 
rate would  the  determination  of  their  distance  in  scale  divi- 
sions be  if  made  from  a  single  observation  of  the  lines  a  and  h 
upon  the  scale,  than  though  the  distance  of  two  neighboring 
lines  were  directly  noted  ?     How  would  you  compute  the  dis- 
tance in  the  former  case  ? 

CHAPTER   II 

9.  At  the  ends  of  a  wire  or  cord  are  suspended  two  equal 

weights,  stretching  it  horizontally  be- 
tween the  two  pulleys  a  and  6.  A 
third  weight  equal  in  mass  to  each 
of  the  others  is  hung  from  the  cord 
midway  between  a  and  b.  In  what 
position  will  the  system  come  to 

I"1]  rS  rest?     (See  Arts.  12  and  13.) 

10.   If   in  the  above   example  we 

add  weights  between  the  pulley  until  the  angle  n  is  90°,  what 

will  be  the  relation  of  the  weights  at 

the  end  and   at  the  middle  of  the 

cord? 

11.  Find  graphically  the  resultant 
of  the  forces  AB,  AC,  AD. 

12.  Find    graphically  two    forces D 

that  are  equivalent,  when  acting  together 
A  B   upon  the  point  A,  to  the  force  AB. 

13.    Can  a  cable  or  wire  be  stretched 
horizontally  until  it  does  not  sag  at  all  ?     Explain. 

14.  The  string  of  a  violin  or  guitar  may  be  stretched  upon  the 
instrument  almost  to  the  breaking  point,  yet  it  can  be  readily 
displaced  laterally  by  a  touch  of  the  finger.  Why  ? 


MECHANICS  3 

15.  A  weight  hangs  vertically  by  a  wire  from  a  point  A. 
To  the  wire  a  string  is  attached  by  means  of  which  a  lateral 
pull  is  exerted.     Show  graphically  the  lateral   pull   for   any 
given  position ;  also  the  force  upon  the  wire  above  the  point 
of  attachment. 

16.  In  the  above  case,  will   the  pull  upon  the  string  be 
greater  when  the  latter  is  horizontal  or  when  its  direction 
bisects  the  angles  between  the  upper  and  lower  portions  of 
the  wire?     Why? 

17.  An  oarsman  can  propel  a  boat  in  still  water  with  a 
speed  of  3  m.  per  second.     If  he  rows  at  that  speed  at  right 
angles  to  the  current  of  a  stream  which  flows  at  the  rate  of 
4  m.  per  second,  how  far  from  his  starting  point  will  he  be  in 
one  minute  ?     Give  a  diagram. 

CHAPTER   III 

18.  In  Galileo's   experiment  (Art.  24),  what  must  be  the 
angle  of  the  inclined  plane  to  reduce  the  component  force  of 
gravity  tending  to  produce  motion  to  one-half  ? 

19.  A  ball  upon  an  inclined  plane  traverses  a  distance  of 
100  cm.  from  rest  during  one  second.     How  far  will  it  travel 
in  10  seconds  ?     (See  Art.  26.*) 

20.  Under  the  conditions  of  Question  19,  what  will  be  the 
velocity  of  the  ball  at  the  end  of  one  second  ?   of  10  seconds  ? 

21.  A  body  falling  freely  through  space  traverses  a  distance 
of  450  cm.  in  one  second.     What  will  be  its  velocity  at  the 
end  of  five  seconds? 

22.  A  ball  dropped  from  a  balloon  reaches  the  earth  in  10 
seconds.     The  acceleration  due  to  gravity  is  980.  cm.f     What 
is  the  height  of  the  balloon  in  meters  ? 

*  In  this  and  all  subsequent  questions  upon  falling  bodies,  the  resist- 
ance of  the  air  is  to  be  neglected. 

t  In  subsequent  questions,  the  acceleration  due  to  gravity  will  be 
designated  by  the  symbol  g.  Its  value  is  to  be  taken  as  980  cm.  un- 
less otherwise  specified. 


4  MECHANICS 

23.  In  a  certain  locality  gravity  produces  an  acceleration 
of  980  cm.    What  is  the  force  of  gravity  in  dynes  upon  a  mass 
of  1000  g.  ? 

24.  A  cannon  ball  weighs  10,000  g.     If  it   takes  y^  of 
a  second  to  bring  it  to  its  full  velocity  at  the  muzzle  of  the 
gun  when  fired,  and  that  velocity  is  500  m.  per  second,  what 
is  the  average  force  of  the  explosive  in  dynes  ? 

25.  At  the  surface  of  the  moon,  the  acceleration  due  to 
gravity  is  16J  per  cent  of  that  at  the  surface  of  the  earth. 
What  is  the  force  of  gravity  there  upon  a  mass  of  1  g.  ? 

CHAPTER   IV 

26.  From  a  point  122.5  m.  above  the  surface  of  a  lake,  a 
gun  is  fired  horizontally.     The  velocity  of  the  bullet  when  it 
leaves  the  gun  is  400  in.  a  second.     At  what  distance  meas- 
ured along  the  water,  from  a  point  vertically  below  the  gun, 
will  the  bullet  strike  the  surface  of  the  lake?     (The  value 
of  g  is  980  cm.) 

27.  How  many  seconds  will  elapse  after  the  firing  of  the 
gun  described  in  Question  26  before  the  bullet  will  strike  the 
water  ?     Draw  a  diagram  showing  its  position  at  the  end  of 
each  successive  second. 

28.  Assuming  the  conditions  of  Questions  26  and  27,  con- 
sider the  gun  to  be  pointed  upwards  at  an  angle  of  30°  with 
the  horizon.    Draw  a  diagram  showing  the  course  of  the  bullet. 
Eepeat  for  angles  of  45°  and  60°.    (See  Art.  32.) 

29.  A  bullet  is  shot  vertically  upwards.      Neglecting  the 
resistance  of  the  air,  how  would  its  velocity,  when  under  the 
influence   of   gravity  it   has   returned   again  to  the   level   of 
the  gun,  compare  with  its  initial  velocity  ?     Explain. 

30.  A  bullet  is  shot  horizontally  from  the  mouth  of  "a  gun, 
and  another  at  the  same  instant  is  dropped  vertically  from  the 


MECHANICS  0 

same  height  above  the  ground.  Show  that  if  the  ground  is 
level  they  will  reach  it  at  the  same  instant  of  time.  Give 
a  diagram. 

31.  By  means  of  a  spring  gun.  mounted  vertically  upon  the 
deck  of  a  moving  vessel,  a  ball  is  thrown  upwards.     What 
kind  of  a  curve  will  its  path  be  ? 

CHAPTER   V 

32.  If  the  length  of  a  pendulum  beating  seconds  in  a  certain 
locality  be  99  cm.,  how  long  a  pendulum  would  make  a  single 
oscillation  in  -fa  of  a  second ;   in  one  minute  ? 

33.  A  clock  with  seconds  pendulum  keeps  accurate  time 
at  sea  level  in  latitude  45°.     If  moved  to  the  equator  with- 
out disturbing  its  adjustment,  will  it  gain  or  lose  and  how 
much  per  day  ?     (See  Arts.  27  and  42.) 

34.  If  such  a  clock  be  taken  to  a  mountain  top,  will  it  gain 
or  lose  ?     Why  ?     To  restore  it  to  its  proper  rate  at  the  higher 
locality,  must   the   pendulum   be    lengthened   or   shortened  ? 
Why? 

35.  The  value  of  g  on  the  surface  of  the  moon  is  about 
162  cm.     How  long  must  a  pendulum   be   to   beat  seconds 
there  ? 

36.  Find  graphically  the  relative  motions  of  a  pendulum 
bob  during  a  single  oscillation.     [For  this   purpose  draw  a 
circle  and  its  horizontal  diameter.     Divide  the  upper  semicir- 
cumference  into   six  equal  parts.     From   the   ends  of  these 
divisions  drop  perpendiculars  upon  the  diameter.     The  inter- 
sections of  these  perpendiculars  with  the  diameter  will  mark 
the  successive  positions  of  a  bob,  traveling  along  the  diameter, 
after  1,  |,  |-,  etc.,  of  its  single  oscillation  has  been  completed. 
See  Art.  146.] 

37.  From  the  diagram  made  under  Question  36  construct 
a  sine  curve  characteristic  of   the   motion  of  the  pendulum. 


6  MECHANICS 

Draw  a  base  line,  and  divide  it  into  equal  parts.  Each  of 
these  corresponds  to  1  of  a  single  oscillation.  Construct  your 
curve  by  an  application  of  Art.  47. 

38.  If  in  the  experiment  described  in  Art.  48  a  smoked 
cylinder  be  substituted  for  the  plate,  and  the  former  be  re- 
volved upon  an  axis  parallel  to  the  plane  of  oscillation  of  the 
pendulum,  one  revolution  for  each  single  oscillation,  what  will 
be  the  form  of  the  tracing  ? 

CHAPTER   VII 

39.  If  the  bob  of  the  pendulum  shown  in  Fig.  52  weighs 
1000  g.,  and  the  vertical  distance  be  is  10  cm.,  how  much  work, 
in  ergs,  must  be  done  to  lift  the  bob  from  a  to  b  ?     [The  force 
of  gravity  upon  1  g.  of  matter  is  980  dynes.] 

40.  If  the  pendulum  in  Question  39  is  released  at  6,  what 
velocity  will  the  bob  require  when  it  swings  past  the  point  a, 
and  what  will  be  its  kinetic  energy  in  ergs  ? 

41.  Show   that   when   the  pendulum   in   Question  39   has 
reached  the  end  of  its  upward  movement  at  c,  it  has  gained  an 
amount  of  potential  energy  equal  to  the  kinetic  energy  which 
it  possessed  by  virtue  of  its  velocity  at  the  point  a. 

42.  A  projectile  weighs  2000  g.     Its  velocity  is  1000  cm. 
per  second.     How  much  work  will  it  do  in  coming  to  rest? 
If  its  energy  could  all  be  applied  to  lifting  a  kilogram  weight 
against   gravity,  to  what   height  would   it  be  raised?     Let 
g  =  980  cm. 

43.  The  work  required  to  lift  10  kg.  to  a  height  of  10  m. 
against  gravity  is  how  many  kilogram-meters?     Where  g  is 
980  cm.,  how  many  ergs  is  this  equivalent  to  ? 

44.  To  how  many  ergs  is  a  kilogram-meter  equal  on  the  sur- 
face of  a  planet  where  g  is  100  cm.  ? 

45.  What  would  be  the  result  in  Experiment  11  of  using  a 
wire  instead  of  the  rope  described  under  Section  (3)?     Why  ? 


MECHANICS  7 

CHAPTER   VIII 

46.  In  Fig.  45  suppose  Pl  to  be  100  g.  and  P2  (including  the 
pulley)  to  be  200  g.     If  y  =  980  cm.,  what  will  be  the  force 
upon  the  hook  which  sustains  the  cord  c  ?     What  will  be  the 
force  upon  the  screw  which  holds  the  pulley  A  ? 

47.  If  the  pulley  weight  P1  (as  above)  fall  1  in.,  what  work 
will  it  perform  ? 

48.  In  Fig.  47  what  weight  must  be  attached  at  b  to  give 
under  the  action  of  gravity  the  force  indicated;    i.e.  50,000 
dynes  ? 

49.  Which  class  of  lever  is  represented  in  the  crowbar  (used 
in  prying),  the  crowbar  (used  in  lifting),  the  plyers,  the  scis- 
sors, the  nut  cracker,  the  human  arm  (used  in  lifting)  ?     Why 
do  we  find  it  difficult  to  lift  even  a  moderate  weight  with  the 
arm  extended  horizontally  ? 

50.  Under  what  circumstances  is  the  wheel  and  axle  prefer- 
able to  a  common  lever  with  the  same  ratio  of  lever  arms  ? 

51.  In  Fig.  54  show  that  the  work  required  to  raise  the  ball 
from  a  to  b  along  the  plane  is  the  same  as  that  necessary  to 
lift  it  vertically  from  c  to  b. 

52.  In  what  sort  of  equilibrium  (stable,  unstable,  or  indif- 
ferent) is  a  cone  balanced  upon  its  apex;  a  wedge  balanced 
upon  its  edge ;  a  cylinder  resting  upon  a  plane ;  a  ball  resting 
upon  a  plane ;    a  cylinder  suspended  by  means  of  a  support 
through  its  axis ;  a  stool  with  three  legs  on  the  floor ;  a  stool 
with  two  legs  on  the  floor  ? 

53.  How  would  you  find  the  center  of  mass   of   a  horse- 
shoe? 

54.  Given  a  disk  placed  upon 
an  inclined  plane.     If  its  cen- 
ter of  mass  is  at  a,  what  will  it 

do  if  released  ?     If  at  b  ?     If  at  c  ? 


8  MECHANICS 

55.  In  a  balance  if  the  milled  nut  above  the  axis  of  sup- 
port at  0  (Fig.  64)  be  raised,  what  will  be  the  effect  upon  the 
sensitiveness  ?     What  will  be  the  effect  upon  the  rapidity  of 
movement  of  the  balance  ?     Why  ?     If  the  nut  be  raised  too 
high,  e.g.  until  the  center  of  mass  is  above  the  axis  of  support, 
what  will  be  the  result  ? 

56.  The  arms  of  a  balance  differ  in  length  by  one  part  in  a 
thousand.     A  body  placed  at  the  end  of  the  longer  arm  just 
balances  a  kilogram  weight  placed  at  the  end  of  the  shorter. 
What  is  its  correct  weight  ?     (Solve  by  applying  the  principle 
of  moments ;  Art.  62.) 

CHAPTER   X 

57.  If  in  Experiment  16  a  disk  of  wood,  slate,  or  porcelain 
be  substituted  for  the  glass,  what  would  be  the  effect  upon  the 
result  of  the  experiment  ? 

58.  To  measure  the  attractive  force  between  water  and  a 
solid  by  the  method  of  Experiment  16,  what  sort  of  substance 
would  have  to  be  chosen  for  the  surface  of  the  disk  ? 

59.  With  the  apparatus  in  Fig.  69  we  find  the  weight  m^ 
which  the  weight  m2  is  just  capable  of  maintaining  in  uniform 
motion  upon  the  plane,  to  be  six  times  as  great  as  m.     What  is 
the  coefficient  of  sliding  friction  ? 

60.  With  the  apparatus  in  Fig.  70  we  find  by  increasing  the 
pitch  of  the  plane  very  carefully  that  the  weights  begin  to  slip 
when  the  angle  is  such  that  AC  (Fig.  71)  is  four  times  BO. 
What  is  the  coefficient  of  starting  friction  ? 

61.  The  force  necessary  to  move  10  kg.  along  a  level  sur- 
face is  found  to  be  1,960,000  dynes.     What  is  the  coefficient 
of  friction  ?     [g  =  980  cm.] 

62.  Why  will  a  thick  layer  of  a  liquid  act  as  a  lubricant 
while  a  very  thin  film  of  the  same  liquid  will  hold  the  sur- 
faces, between  which  it  lies,  as  if  cemented  ? 


MECHANICS 


CHAPTER    XI 

63.  Which  possesses  more  nearly  perfect  elasticity  of  form, 
lead  or  steel  ?     Dry  wood  or  unseasoned  wood  ? 

64.  A  wire  is  100  cm.  long  and  0.5  cm.  in  diameter.     When 
stretched  by  the  application  of  10,000,000  dynes  it  increases 
in  length  0.5  cm.     What  is  the  value  of  the  stretch  modulus  ? 
(See  Art.  91.) 

65.  Two  wires  are  of  the  same  length  and  same  diameter. 
Both  are  placed  under  equal  stress.     One  stretches  twice  as 
much  as  the  other.     What  is  the  relation  between  the  stretch 
moduli  ? 

66.  A  certain  force   suffices   to   stretch   a  wire  of  0.1  cm. 
diameter  so  as  to  produce  an  elongation  of  1  cm.     What  force 
will  produce  the  same  elongation  in  a  wire  of  the  same  length 
and  same  material  but  1.0  cm.  in  diameter  ? 

67.  Two  rods  are  2  cm.  and  4  cm.,  respectively,  in  diameter, 
and  of  equal  length.     One  end  of  each  is  rigidly  clamped  and 
forces  are  applied  at  the  free  ends  to  twist  the  bars.     Compare 
the  moments  of  the  forces  which  will  twist  the  two  bars  equally. 

68.  Along  the  surface  of  a  rod  a  white  longitudinal  line  is 
drawn  with  chalk.     One  end  of  the  rod  is  clamped,  and  the 
other  is  twisted  through  an  angle  of  180°.     What  will  be  the 
position  of  the  chalk  mark  upon  the  twisted  rod  midway  from 
the  clamped  end  to  the  twisted  end  ?     One  quarter  way  from 
the  clamped  end  ? 

CHAPTER   XII 

69.  The  principal  force  acting  upon  a  vessel  of  liquid,  at 
rest  upon  the  surface  of  the  earth,  is  that  of  gravity.     From 
the  position  assumed  by  the  surface  of  the  liquid,  what  must 
we  conclude  concerning  the  direction  in  which  gravity  acts  ? 


10  MECHANICS 

70.  In  Experiment  23,  after  the   pressure  applied  at  the 
funnel  has  been  removed,  will   the  air  within  the  indicator 
bulb  return  precisely  to  its  former  volume  ?     (See  Art.  88.) 

71.  In  Fig.  86  if  the  diameter  of  the  piston  A  is  20  cm. 
and  that  of  a  is  1  cm.,  how  far  must  a  be  lowered  to  raise  A 
1  cm.  ?     Friction  being  neglected,  what  weight  on  A  will  1  kg. 
on  a  sustain  ? 

72.  Show  that  in  the  case  of  the  hydraulic  press,  where  a 
large  weight  is   raised,  the  whole  equivalent  of  work   must 
always  be  performed. 

73.  Into  a  glass  jar  containing  mercury  a  glass  tube  open 

at  both  ends  is  plunged.  If  water  be  poured  into 
the  jar,  will  the  mercury  rise  within  the  tube  ? 
If  so,  how  high  ?  (The  density  of  mercury  is 
13.6  times  that  of  water.)  If  water  be  poured 
into  the  tube  instead  of  into  the  jar,  what  will 
the  result  be  ? 


74.   In  Experiment  24,  what  will  be  the  result 
if  a  large  vessel  such  as  a  tub  were  substituted 
for  the  jar  ? 

75.  In  Experiment  24,  what  will  be  the  result  of  substi- 
tuting an  oil  of  three-fourths  the  density  of  water  in  the  jar  ? 

76.  In  Experiment  24,  what  would  be  the  result  of  using 
mercury  instead  of  water  in  the  U-shaped  tube  ? 

77.  A  water-tight  cask  is  strong  enough  to  sustain  an  out- 
ward pressure  of  5000  g.  on  each  square  centimeter  of  its  sur- 
face.    A  long  vertical  tube,  1  sq.  cm.  in  cross-section,  is  fitted 
to  the  head  of  the  cask.     The  cask  having  been  filled  with 
water,  we  continue  to  pour  water  into  the  tube  until  the  cask 
bursts.     How  high  a  column  of  water  is  required  ? 

78.  In  the  above  question,  what  would  be  the  height  of  the 
column  provided  the    diameter   of    the  tube   were   10  cm.  ? 
Explain. 


MECHANICS  11 

79.  A  body  submerged  in  water  loses  one-half  its  weight. 
What  is  its  density  ?     (Express  the  density  as  defined  in  Art. 
107,  i.e.  in  grams  per  cubic  centimeter  of  volume.) 

80.  A  block  of  wood  floats  three-fourths  submerged  in  water. 
What  is  its  density  ? 

81.  The  block  mentioned  in  Question  80  floats  entirely  sub- 
merged in  a  certain  oil.     What  is  the  density  of  the  oil  ? 

82.  The   density  of  ice  is  0.917 ;  that  of  sea  water,  1.026. 
What  proportion  of  a  floating  iceberg  is  submerged  ? 

83.  A  metal  ball  weighs  100  g.     We  suspend  it  by  a  string 
and  dip  it  in  the  water  of  a  beaker  which  is  placed  upon 
the  scale  pan  of  a  balance.     When  the  ball  is  submerged  with- 
out touching,  the  bottom  of  the  beaker,  the  latter  is  found  to 
gain  20  g.  in  weight.     What  is  the  density  of  the  ball  ?     (See 
Art.  104.) 

84.  In  the  cylinder  and  bucket  experiment  (Art.  103)  we 
fill  the  bucket  with  alcohol  instead  of  water.     Equilibrium  is 
reached  with  the  cylinder  •£$  submerged  in  water.     Find  the 
density  of  the  alcohol. 

CHAPTER   XIII 

85.  In  Experiment  27  an  aluminum  ball  is  used.     It  weighs 
100  g.  in  air,  and  its  density  is  2.6.     What  will  it  weigh  in 
water  ? 

86.  A  metal  ball  weighs  1000  g.     It  is   suspended   by  a 
wire  and  carefully  lowered  into  a  cylindrical  vessel  of  water. 
When  the  ball  is  fully  submerged,  the  rise  in  the  level  of  the 
liquid  in  the  cylinder  is  noted  and  the  diameter  of  the  latter 
is  measured.     Show  how  from  these  observations  the  density 
of  the  ball  may  be  computed. 

87.  Why  are  hydrometers  (as  shown  in  Fig.  99)  constructed 
with  long  and  narrow  necks  ? 


12  MECHANICS 

88.  A  Fahrenheit  hydrometer  weighs  50  g.     When  floating 
in  water  20  g.  must  be  added  to  submerge  it  to  the  mark  upon 
the  neck.     In  a  solution  of  brine  30  g.  are  necessary  to  sub- 
merge  it   to  the   same   point,  while  in  an  oil   but  10  g.  are 
required  upon  the  scale  pan.     What  are  the  specific  gravities 
of  .the  brine  and  of  the  oil  ? 

89.  In  Experiment  28  a  piece  of   glass  weighing  10  g.  is 
placed  upon  the  upper  pan  of  the  hydrometer.     The  addition 
of  9  g.  brings  the  pointer  to  the  surface  of  the  liquid.     When 
the  glass,  the  density  of  which  is  2.7,  is  placed  upon  the  lower 
pan,  what  weight  must  be  placed  upon  the  upper  pan  to  sub- 
merge the  hydrometer  to  the  proper  point  again  ? 

90.  A  certain   specific   gravity   flask   will   hold  100  cc.   of 
water.     After  pouring  into  it  100  g.  of  sand  it  is  found  possi- 
ble to  add  66  g.  of  water.     WTiat  is  the  density  of  the  sand  ? 

91.  Which  of  the  elements  mentioned  in  the  table  in  Art. 
114  would  sink  if  thrown  into  mercury  ?     Which  would  float 
upon  water  ? 

CHAPTER  XIV 

92.  Draw  a  picture,  showing  the  form  which  a  drop  of 
water,  when  inclosed  in  a  glass  tube  of  narrow  bore,  would 
assume.     Indicate  particularly  the  form  of  the  surface  film, 
applying  the  statements  concerning  the  properties  of  the  film 
given  in  Chapter  XIV.     Verify  your  drawing  by  observations 
upon  water  in  a  tube  of  about  1  mm.  diameter. 

93.  Make  a  drawing  as  in  Question  90,  assuming  the  liquid 
to  be  mercury  instead  of  water. 

94.  A  tube  of   small  bore  with  both  ends  open  is  dipped 
vertically  into  water  and  then  withdrawn.      A  considerable 
quantity  of  water  will  remain  in  the  vertical  open  tube  in 
spite  of   the   attraction  of   gravity.     Why  ?     Illustrate  your 
answer  by  a  diagram  and  verify  by  observations. 


MECHANICS  13 

95.  Why  does  the  liquid  rise  higher  in  tubes  of  small  bore 
than  in  tubes  of  large  bore  ? 

96.  If  the  smaller  tube  in  Fig.  109  were  cut  oft'  below  the 
level  of  the  liquid  within  the  tube,  would  there  be  an  overflow 
at  the  open  end  ?     Explain. 

97.  In  the  case  of  glass  dipped  into  water,  is  the  angle  of 
contact  greater  or  less  than  90°  ? 

Each  member  of  the  class  should  be  provided  with  a  piece  of  glass 
tubing  about  10  cm.  long  and  1  or  2  mm.  in  diameter,  with  which  to  test 
his  answers  to  the  questions  upon  this  chapter. 

98.  Two   connecting   glass   vessels   hold    respectively   1   1. 
and  9  1.     The  smaller  contains  a 

O    I  ITFRft 

gas  under  a  pressure  of  1000  g. 

per  square  centimeter  of  surface.    /  \        O 

It  is  prevented  from  passing  into  B- 

the  larger  vessel,  which  is  empty, 

by  a  stopcock.     If  the   stopcock 

is  opened,  what  will  be  the  pressure  after  the  gas  has  filled 

both  vessels  ? 

99.  If  in  Torricelli's  experiment  water  were  used  instead  of 
mercury,  how  long  a  tube  would  be  required  ? 

100.  Upon  a  mountain  peak  the  barometer  reads  38  cm.     If 
a  liter  flask  be  filled  with  air  at  the  level  of  the  sea,  carried  to 
the  peak  and  there  opened,  how  much  air  will  escape  ?     What 
will  the  air  which  remains  within  the  flask  weigh  ?     (Consult 
the  table  in  Art.  124.) 

101.  What  is  the  mass  of  a  column  of  mercury  1  cm.  in 
cross-section  and  76  cm.  high  ?     From  your  answer  deduce  the 
pressure  in  grams  per  square  centimeter,  also   in   dynes  per 
square  centimeter,  to  which  all  surfaces  which  are  exposed  to 
the  atmosphere  at  the  level  of  the  sea  are  subject.     Reduce 
your  answer  likewise  to  pounds  per  square  inch. 

102.  Suppose  the  upper  end  of  the  tube  in  Fig.  125  to  be 
sealed,  and  pressure  to  be  applied  at  h  until  the  air  inclosed 
above  h  is  reduced  to  T-i^  of  its  initial  volume.    What  pressure 


14  MECHANICS 

will  be  required  (1)  in  atmospheres,  (2)  in  grams,  per  square 
centimeter  ? 

CHAPTER   XVI 

103.  The  expansion  of  copper  when  heated  is  much  greater 
than  that  of  platinum.     If  a  strip  of  copper  be  soldered  back 
to  back  with  a  strip  of  platinum  and   the  double  strip  thus 
formed  be  heated,  what  will  happen  ? 

104.  If  a  glass  bulb  be  entirely  tilled   with   mercury  and 
closed,  what  will  happen  on  heating  it  ?     Why  ? 

105.  Does  the  change  due  to  heating  in  the  diameter  of  the 
tubes  used  in  Eegnault's  experiment  (Art.  134)  need  to  be  con- 
sidered in  determining  the  expansion  of  the  liquid  ?     Explain. 

106.  If  the  bulb  in  Fig.  134  be  cooled  and  suddenly  placed 
in  the  hot  bath,  the  first  movement  of  the  mercury  will  be 
downward.     Why  ? 

107.  In  the  Fahrenheit   thermometers  commonly  used  for 
household  purposes,  the  ice  point  is  at  32°  and  the  melting  point 
at  212°.     One   degree   centigrade  equals   how   many   degrees 
Fahrenheit  ?     (Express  the  ratio  as  a  common  fraction.) 

108.  When  the  Fahrenheit  thermometer  reads  90°,  what  is 
the  temperature  in  degrees  centigrade  ?    (See  Question  107.) 

109.  When    the    Fahrenheit    thermometer    indicates     ten 
degrees  below  zero,  what  is  the  centigrade  reading  ? 

110.  The  temperature  +  50°  C.  (centigrade)  corresponds  to 
what  point  011  the  absolute  scale  ?     (See  Art.  140.) 

111.  A  volume  of  gas  at  0°C.  is  1  1. ;  at  what  temperature 
will  it  expand  to  2  1.    if   the   pressure   be   maintained   con- 
stant ? 

112.  A  liter  of  gas  at  0°C.  is  heated  to  100°  C.     How  much 
must   the  pressure  be  increased  to  restore  it  to  its  original 
volume  ? 


MECHANICS  15 


CHAPTER    XVII 

113.  Why  are  the  temperatures  of  the  hot  and  cold  water  in 
Experiment  37  taken  equally  above   and   below  that  of  the 
room  ? 

114.  If  10  g.  of  water  at  50°  C.  be  mixed  with  100  g.  of 
water  at  10°  C.,  what  will  the  final  temperature  be  ? 

115.  If  100  g.  of  water  at  50°  C.  be  mixed  with  100  g.  of 
another  liquid  (not  water)  at  10°,  and  the  final  temperature 
be  40°,  what  is  the  thermal  capacity  of  the  liquid  compared 
with  that  of  water  ? 

116.  How  much  mercury,  heated  to  100°  C.,  must  be  mixed 
with  1  kg.  of  water  at  0°  to  make  the  temperature  of  the 
mixture  10°?     (For   specific   heat   of  mercury   see   table   in 
Art.  150.) 

117.  Three  kilograms  of  lead  are  heated  to  100°  and  are 
plunged  into  1  kg.  of  water  at  20°  C.      They  produce  a  rise 
of  temperature  to  27°.     What  is  the  specific  heat  of  the  lead  ? 

118.  A  quantity  of  boiling  water  is  poured  into  the  cavity  of 
an  ice-block  calorimeter.     It  melts  200  g.  of  ice.     What  is  the 
mass  of  the  hot  water  ?     (See  Art.  151.) 

119.  A  block  of  copper  weighing  1  kg.  is  heated  to  100°  C. 
It  is  then  placed  in  a  cavity  in  an  ice  block.     How  much  ice 
will  it  melt  ? 

120.  How   does   the  amount  of  heat  energy  necessary  to 
evaporate  a  kilogram  of  water  at  100°  C.  compare  with  that 
required  to  raise  that  amount  of  water  from  the  melting  point 
of  ice  to  100°  C.  ? 

121.  In  Experiment  41,  if  the  lamp  under  the  flask  were  ex- 
tinguished and   the  apparatus  were   allowed   to  cool  without 
removing  the  delivery  tube   from  the  beaker  of   water  (Fig. 
147),  what  would  take  place  ?     Explain. 


16  MECHANICS 

CHAPTER   XVIII 

122.  In  what  respect  does  paraffin  differ  from  water  in  the 
phenomena  of  fusion  ?     (See  Experiment  42.) 

123.  A  massive  steel  cylinder  is  bored  and  fitted  with  a 
screw.     The  interior  is  filled  with  ice  at  0°  C.     The  screw  is 
then   turned   so   as   to   increase  the   pressure.     What  is  the 
result  ?     (See  Art.  160.)     If  the  pressure  is  1000  atmospheres, 
at  what  temperature  will  the  water  freeze  within  the  cylinder  ? 

124.  Describe  the  process  of  boiling. 

125.  Why  in  Experiment  43  will  boiling  cease  when  the 
stream  of  cold  water  is  turned  off? 

126.  What  cools  the  water  described  in  Art.  163  to  the 
freezing  point?     (See  Art.  165.) 

127.  Why  does  a  moistened  hand  feel  cool?     Why  cooler 
in  the  wind  ?     Why  much  colder  if  moistened  with  ether  than 
with  water  ? 

128.  Why  does  the  liquid  described  in  Art.  166  assume  the 
form  of  a  spheroid  ?     (Refer  back  to  Chapter  XIV.) 

129.  From  the  phenomena  described  in  Arts.  166  and  167, 
what  inference  may  be  drawn  concerning  the  proper  explana- 
tion of  the  experiment,  sometimes  tried  with  success,  of  walk- 
ing barefoot  on  red-hot  metal  without  burning  the  previously 
moistened  feet  ? 

CHAPTER   XIX 

130.  What  is  the  source  of  the  heat  energy  developed  in 
Experiment  47? 

131.  What  becomes  of  the  energy  expended  to  compress  the 
gas  in  Experiment  48  ? 

132.  A  mass  of  iron  weighing  1000  kg.  is  transported  to  a 
height   of   100  m.     What  work,   in   ergs,   is   expended?     If 


MECHANICS  17 

allowed  to  fall  freely  through,  the  same  distance,  how  many 
calories  would  be  developed  by  the  expenditure  of  all  the 
energy  of  its  fall  ? 

133.  A  locomotive  engine  weighing  100,000  kg.  is  derailed 
and  plunges  into  an  embankment.     If  the  entire  energy  of  its 
motion,  the  velocity  of  which  was  2600  cm.  per  second,  were 
converted  into  heat,  how  much  ice  would  it  melt  ? 

134.  A  kilogram  of  water  falls  4000  cm.     If  all  the  energy 
thus  developed  were  converted  into  heat,  how  many  degrees 
would  it  warm  the  water  ? 

CHAPTER   XX 

135.  When  the  glass  stopper  of  a  bottle  sticks  fast,  it  can 
often  be  removed  by  warming  the  neck  of  the  bottle.     Why  ? 

136.  In  Experiment  50,  why  must  the  heat  be  applied  at  the 
top  of  the  vessel  of  water  ?     (Consult  Art.  179.) 

137.  If  a  printed  page  is  held  in  the  focus  of  a  "burning 
glass,"  the  ink-covered  portions  will  be  burned  away,  leaving 
the  white  surfaces  unscorched.     Why  ? 

138.  If  a  piece  of  black  paper  be  laid  upon  the  surface  of 
ice,  the  ice  under  it  will  be  found  to  melt  more  rapidly  than 
elsewhere.     Why  ? 

139.  If  with  a  thermopile  arranged  between  two  blocks  of 
clear  ice,  as  in  Fig.  171,  we  hold  a  glass  flame  in  front  of  one 
of  the  blocks,  there  will  be  immediate  indication  that  the  face 
of  the  thermopile  on  that  side  is  warmed.     By  which  of  the 
three  processes  mentioned  in  Art.  175  is  the  heat  transmitted  ? 

CHAPTER   XXI 

140.  If  in  Experiment  60,  Section  d,  while  the  vulcanite  rod 
is  still  held  near  the  plate  of  the  electroscope,  an  electrified 
glass  rod  be  likewise  brought  near,  will  the  gold  leaves  diverge 
further,  or  will  they  come  together  ?     Why  ? 


18  MECHANICS 

141.  Why  are  gold  leaves  used  in  the  electroscope  rather 
than  strips  of  any  other  metal? 

142.  An  electroscope  has  been  charged  positively  by*con- 
tact  with  an  electrified  glass  rod.     Describe  and  explain  in' 
terms  of  the  theory  of  two  fluids  what  occurs  when  an  electri- 
fied vulcanite  rod  is  brought  near. 

143.  An  electroscope  is  given  a  permanent  charge  by  induc- 
tion from  a  positively  electrified  glass  rod.     Describe  and  ex- 
plain what  occurs  when  the  same  rod  is  subsequently  brought 
near. 

CHAPTER  XXII 

144.  Contrast  what  is  called  the  conduction  of  electricity 
(Experiment  61)  with  the  transmission  of  heat  by  conduction 
(Experiments  49,  etc.),  as  regards  promptness  of  effect. 

145.  Should  the  containing  vessel  of  an  electroscope  and  the 
materials  which  support  the  rod  and  leaves  be  conductors  or 
non-conductors  of  electricity  ?     Why  ? 

146.  In  Art.  202  it  is  stated  that  all  kinds  of  matter  are 
capable  of  electrification.     Why,  then,  will  a  metal  rod  held  in 
the  hand  and  rubbed  fail  to  show  a  charge  ?     What  precaution 
must  be  taken  to  make  it  do  so  ? 

147.  Is  glass  when  rubbed  always    positively  electrified  ? 
(See  Art.  202.) 

148.  From  an  inspection  of  Faraday's  electrostatic  series, 
what  should  you  expect  if  you  were  to  rub  fur  and   glass 
together?     What  if  you  were  to  rub  sulphur  with  fur? 

149.  Does  Faraday's  series  throw  any  light  upon  the  choice 
of  sodium  amalgam  rather  than  silk  as  a  rubber  in  the  "  plate  " 
electrical  machine  ? 

150.  If  in  an  electrophorus  we  substitute  glass  for  the  vul- 
canite plate  and  excite  with  silk,  what  kind  of  a  charge  will  be 
obtained  on  the  metal  plate  after  the  usual  operations  have 
been  performed? 


MECHANICS  19 


CHAPTER   XXIII 

151.  Why  would  not  silk  serve  as  well  as  linen  in  the  con- 
struction of  a  Faraday  bag  ?     (Art.  210.) 

152.  Two  small  equally  charged  spheres  are  1  m.  apart. 
They  repel  each  other  with  a  force  of  1  dyne.     (Electrical 
action  in  such  a  case  is  inversely  as  the  square  of  the  distance.) 
What  number  of  units  of  electricity  are  there  on  each  ? 

153.  In  Experiment  65,  why  does  not  the  charge  continue  to 
reside  upon  the  entire  surface  of  the  curtain  when  rolled  ? 

154.  Why  is  a  silk  thread  used  in  Experiment  65  ?     Could 
such  a  thread  be  substituted  for  the  fine  wire  which  connects 
the  curtain  with  the  proof  plane  ?    Would  a  linen  thread  serve 
in  the  latter  case  ?     Explain. 

155.  How  does  the  electrometer  become  charged  in  Experi- 
ment 65  ? 

156.  A  metal  sphere  is  brought  near  to  a  large  conductor 
which  is  charged  negatively.    Show  by  a  diagram  the  distribu- 
tion of  the  induced  charge  upon  the  sphere. 

157.  The  metal  sphere  after  being  connected  for  a  moment 
with  the  earth  is  insulated  and  removed  to  a  distance  from 
the  charged  conductor.     What  is  then  its  electrical  condition  ? 
How  would  you  test  its  condition  ? 

CHAPTER  XXIV 

158.  Why  are  not  the  tinfoil  coatings  of  the  Ley  den  jar 
continued  to  the  top  of  the  jar  ? 

159.  Given  two  Ley  den  jars  of  the  same  size  and  kind  of 
glass.     The  glass  of  one  of  the  jars,  however,  is  twice  as  thick 
as  that  of  the  other.     Which  will  have  the  greater  capacity  ? 

160.  Given  two   condensers,  each   consisting  of  a  pair  of 
brass  plates  like  those  of  the  air  condenser  (Fig.  209).     Be- 


20  MECHANICS 

tween  the  plates  are  placed  respectively  a  layer  of  paraffin, 
and  a  sheet  of  glass  of  the  same  thickness.  Which  condenser 
will  have  the  greater  capacity  ? 

161.  A  Ley  den  jar  is  placed  upon  a  sheet  of  hard  rubber, 
thus  insulating  the  outer  coating.     The  knob  is  connected  by 
means  of  a  wire  to  the  plate  of  an  electroscope.     The  jar  is 
charged  until  a  considerable  divergence  of  the  leaves  occurs. 
The  outer  coating  is  then  connected  with  the  earth.     What 
will  be  the  effect  upon  the  divergence  ?     Explain. 

162.  In  Fig.  215,  suppose  the  needle  to  be  charged  positively 
and  the  quadrants  act,  to  be  charged  positively.     Describe  the 
movement  of  the  needle. 

CHAPTER   XXV 

163.  Define  the  term  "disruptive  discharge."     Is  lightning 
such  a  discharge  ? 

164.  Describe  the  effect  of  reducing  the   pressure   of  the 
atmosphere  through  which  a  disruptive  discharge  takes  place. 

165.  Explain  the  action  of  the  revolving  mirror.    (Art.  229.) 

166.  In  what  respect  does  a  Geissler  tube  differ  from  the 
vacuum  tubes  used  for  the  generation  of  the  X-rays  ? 

CHAPTER   XXVI 

167.  How  may   the   difference   of    potential    between  the 
metals  of  a  voltaic  cell  be  shown  to  exist? 

168.  What  is  the  difference  between  an  open-circuit  cell,  and 
a  closed-circuit  cell? 

169.  What  is  the   object  of  amalgamating  the  zinc  of  a 
voltaic  cell  ? 

170.  What  are  the  results  of  the  accumulation  of  gas  upon 
the  metals  of  a  voltaic  cell  ? 


OF 

UNIVERSITY  j 
MECHANICS  \  Or,  M\h*/    21 


CHAPTER   XXVII 

171.  Account  for  the  difference  in  the  appearance  of  the 
magnetic  fields  in  Figs.  236  and  237. 

172.  Define  the  term  "  magnetic  pole." 

173.  If  the  current  in  Fig.  239  flow  counter-clockwise,  and 
a  needle  be  inserted  in  the  coil,  with  point  towards  the  ob- 
server, what  sort  of  a  pole  will  be  formed  at  the  eye  end 
of  the   needle  ?      When   floating   on   water,  which   end  will 
tend  to  point  north? 

174.  Why  is  it  always  unlike   poles  which  tend  to  come 
together  in  the  experiment  described  in  Art.  240  (g)  ? 

175.  Can  a  magnet  be  constructed  without  iron  ?   If  so,  how? 

176.  In  what  position  would   the  pull   upon   the   magnet 
needle  (depicted  in  Fig.  243)  due  to  the  earth's  field  be  great- 
est ?     In  what  position  would  the  pull  due  to  the  current  be 
greatest  ? 

177.  A  horizontal  wire  is  stretched  in  a  north-south  direc- 
tion.    A  current  is  sent  through  it  from  north  to  south.     A 
floating  magnet  needle  is  placed  under  the  wire.     What  posi- 
tion will  the  needle  take  ? 

CHAPTER   XXVIII 

178.  Considering  the  earth  to  be  a  magnet,  what  sort  of 
a  pole  is  its  north  pole?      (Like  or  unlike  the  north-seek- 
ing pole  of  a  compass  needle  ?) 

179.  In  a  position  near  the  equator,  what  position  would  a 
dipping  needle  assume  ?     In  what  localities  would  the  needle 
become  vertical  ? 

180.  The  iron  masts  of  ships  are  usually  magnetized  by  the 
earth's    field,  the   repeated  shocks  due  to  waves   facilitating 


22  MECHANICS 

the  effect.    Locate  the  poles  (a)  when  the  ship  has  been  plying 
in  northern  waters ;  (6)  in  the  southern  hemisphere. 

181.  The  iron  pipes  used  in  driving  wells  often  become  mag- 
netized.    Which  pole  (north-seeking  or  south-seeking)  would 
be  found  at  the  top  of  such  a  pipe  ?     Explain  its  occurrence. 

182.  An  umbrella  with  steel  ribs,  which  has  been  long  in 
use,  will  be  found  to  be  a  magnet.      Which  pole  would  you 
expect  to  find  nearest  the  handle  ?    Why  ?    Verify  your  result 
by  experiment. 

183.  The  steel  parts  of  a  watch  are  partially  protected  from 
magnetization  by  using  a  case  of  iron  or  nickel.     Upon  what 
property  of  those  metals  does  their  protecting  power  depend  ? 

184.  Why  are  the  pole  pieces  of  the  electromagnet  depicted 
in  Fig.  253  cut  in  the  form  of  wedges  ? 

185.  If  two  similar  horseshoe  magnets  are  placed  opposite 
one  another,  the  north-seeking  pole  of  the  one  in  contact  with 
the  south-seeking  pole  of  the  other,  they  will  attract  each  other 
strongly.     Trace  the  course  of  the  lines  of  force  in  such  a  case. 

186.  Around  an  iron  ring  a  wire  is  coiled.     If  a  current  be 
sent  through  the  wire,  will   the  iron   be  magnetized  ?     Will 
there  be  poles  ?     Explain  your  answer. 

CHAPTER   XXIX 

187.  Indicate  by  a  diagram  the  direction  in  which  the  elec- 
tric current  must  circulate  in  the  coils  around  the  two  needles 
in  Fig.  257  in  order  that  both  may  tend  to  turn  in  the  same 
direction. 

188.  In  a  given  circuit,  the  total  resistance -of  which  is  main- 
tained constant,  the  electromotive  force  is  increased  tenfold. 
What  will  be  the  effect  upon  the  current  ?     Why  ? 

189.  In  a  given  circuit  the  electromotive  force  remains  con- 
stant and  -the  resistance  is  doubled.     What  is  the  effect  upon 
the  current  ? 


MECHANICS  23 

190.  In  a  given  circuit  we  double  both  electromotive  force 
and  resistance.     What  is  the  effect  upon  the  current  ? 

191.  In  Experiment  80  suppose  ab  to  be  pf  copper,  be  of  iron, 
and  cd  of  platinum.     If  the  diameters  are  as  1:2:3  respec- 
tively, what  deflections  will  be  obtained  ?     (See  table  in  Art. 
263.) 

192.  What  is  the  resistance,  in  ohms,  of  a  copper  wire  1  m. 
long  and  1  sq.  mm.  in  cross-section?     (Compute   from  Arts. 
262  and  263.) 

193.  In  the  Wheatstone  bridge  (Fig.  264),  if  ab  =  10  ohms, 
bc  =  50  ohms,  and  ad=50  ohms,  what  resistance  must  be  given 
to  the  arm  dc  in  order   to  bring  the  galvanometer   to  zero 
deflection  ? 

CHAPTER  XXX 

194.  Why  is  the  copper  wire  in  Experiment  85  (c)  heated  less 
strongly  than  the  platinum  wire  ? 

195.  Given  1  m.  of  iron  wire  and  the  same  length  of  German 
silver  wire.     The  diameters  of  the  two  wires  are  the  same.     If 
traversed  by  the  same  current,  which  will  develop  the  greater 
amount  of  heat  and  in  what  proportion  ? 

196.  For  electrical  cooking,  etc.,  the  heat  is  usually  derived 
from  wires  or   strips  of  metal   heated  by  a  current.     What 
metals  are  best  adapted  for  such  a  purpose,  and  why  ? 

197.  The  current  is  always  sent  through  an  arc  lamp  from 
the  upper  into  the  lower  carbon  pencil.     Why  ? 

CHAPTER  XXXI 

198.  Is  mercury  an  electrolyte  ?     Explain  your  answer. 

199.  Draw  a  diagram  similar  to  Fig.  275.     Suppose  the  cur- 
rent to  pass  through  the  cell  from  left  to  right.     Indicate  by 
labeling  the  kation  and  am  on;  also  what  ion  would  be  set  free 
at  each  in  the  decomposition  of  Na2S04. 


24  MECHANICS 

200.  In  Fig.  279,  twice  as  much  gas  is  shown  to  have  been 
generated  in  the  left-hand  as  the  right-hand  tube.    Which  way 
did  the  current  flow  to  produce  this  result  ?    (The  liquid  in  the 
voltameter  is  supposed  to  be  water.) 

201.  One  ampere  of  current  is  sent   for  one  hour  through 
(1)  a  water  voltameter,  (2)  a  copper  voltameter,  (3)  a  silver 
voltameter.     How  many  cubic  centimeters  of  hydrogen  will  be 
set  free,  and  how  many  grams  each  of  copper  and  silver  ? 


CHAPTER  XXXII 

202.  In  an  apparatus  like  that  shown  in  Fig.  281,  antimony 
forms  the  central  bar  with  bismuth  at  either  end.    The  thermo- 
electric current  flows  from  left  to  right ;  which  is  the  hotter  of 
the  two  junctions  ? 

203.  At  ordinary  temperatures,  which  would   furnish  the 
higher  electromotive  force,  a  therm  o-element  of  German  silver 
—  platinum,  or  of  German  silver  —  iron  ? 

204.  A  thermo-element  consists  of  a  piece  of  platinum  wire 
attached  at  each  end  to  silver  wires.    A  current  is  sent  through 
the  circuit  from  a  battery.    Both  junctions  are  surrounded  with 
ice.     At  which  junction  will  the  most  ice  be  melted  ?    Why  ? 

CHAPTEK   XXXIII 

205.  In  Fig.  284,  suppose  we  are  looking  downward  upon 
the  field.     If  a  wire  represented  by  the  black  cross  line  be 
moved  upwards  through  the  field,  what  will  be  the  direction  of 
the  current  induced  in  the  wire  ?     Show  by  means  of  diagram, 
giving  the  lines  of  force. 

206.  A  current  is  sent  through  the  wire  in  Fig.  284.     The 
force  acting  upon  the  wire  in  consequence  is  upwards.     In 
which  direction  does  the  current  flow  ? 


MECHANICS  25 

207.  A  current  is  sent  through  a  long  cylindrical  spiral 
spring.     Will  the  spring  tend  to  lengthen  or  contract  in  con- 
sequence ?     Answer  by  referring  to  action  of  lines  of  force ; 
give  diagram. 

208.  If  the  upper  pole  of  the  magnet  in  Fig.  291  is  north- 
seeking,  what   must   be  the  direction  of  the  current  in  the 
attracted  wire  ? 

209.  Find  the  direction  of  the  induced  currents  in  the  loop 
of  wire  represented  in  Fig.  294. 

210.  A  thunder  cloud  has  a  positive  charge.    This  when  dis- 
charged produces  a  flash  of  lightning  between  the  cloud  and 
earth.     Surges  of  current  are  thus  induced  in  a  vertical  iron 
pole.     What  will  be  their  directions  ? 

211.  Mention  and  explain  three  methods  of  producing  an 
induced  current  in  a  wire. 


CHAPTER   XXXIV 

212.  The  flash  of  a  firearm  is  seen  five  seconds  before  the 
report  is  heard.     What  is  the  distance  of  the  observer  from 
the  gun  ?     The  temperature  of  the  air  is  20°  C. 

213.  Suppose  in  Question  212  the  wind  to  have  been  blow- 
ing towards  the  observer  at  a  rate  of  20  km.  an  hour.     How 
much  sooner  did  he  hear  the  report  than  though  it  had  been 
blowing  in  the  opposite  direction  with  that  velocity  ? 

214.  During  an  Arctic  winter  Lieutenant  Greely  observed 
the  velocity  of  sound  to  be  as  small  as  305.6  m.  per  second. 
To  what  was  this  low  value  ascribable  ? 

215.  An  observer  is  situated  991  m.  from  a  cliff.      How 
many  syllables  can  he  speak,  at  the  rate  of  two  per  second, 
before  the  echo  reaches  him  ?     The  temperature  of  the   air 
is  0°  C. 


26  MECHANICS 

CHAPTER   XXXV 

216.  A  locomotive  whistle  has  a  pitch  of  256  vibrations  per 
second.     If  sounded  from  a  train  coining  towards  the  observer 
at  a  speed  of  100  km.  an  hour,  will  its  pitch  be  raised  or 
lowered  by  the  motion  ?     How  much  ? 

217.  When  a  bell  is  vibrating  in  the  manner  described  in 
Art.  312  (Fig.  315),  how  many  vibrating  segments  are  there  ? 
Describe  the  position  of  the  nodal  lines. 

218.  What  influence  do  the  finger  tips  placed  upon  the  edge 
of  a  vibrating  plate,  as  for  example  in  Fig.  313,  have  upon  the 
arrangement  of  segments  and  of  nodal  lines  ? 

219.  Of  the  classes  of  instruments  given  in  Art.  308,  which 
is  the  least  musical,  and  why  ? 


CHAPTER  XXXVI 

220.  Into  how  many   segments    is   a  tuning  fork,   which 
vibrates  in  its  simplest  manner,  divided  ? 

221.  In  Fig.  318,  how  many  single  vibrations  of  the  tuning 
fork  must  correspond  to  each  revolution  of  the  disk,  in  order 
that  the  fork,  when  viewed  through  the  slots,  shall  appear 
fixed  in  a  given  position  ? 

222.  The  tracing  of  which  Fig.  322  is  a  full-size  reproduc- 
tion, was  made  with  a  fork  which  performed  256  single  vibra- 
tions  per   second.      At   what   speed   was   the   plate   drawn? 
(Measure  the  curve  with  a  rule  divided  to  millimeters  and 
compute.) 

223.  If  the  tracing  shown  in  Fig.  324  were  made  with  a  pair  of 
forks,  the  higher  of  which  had  a  pitch  of  100  single  vibrations, 
how  many   beats   (approximately)  would   be   produced   each 
second  ? 


MECHANICS  27 


CHAPTER  XXXVII 

224.  A  weight  of  1000  g.  stretches  a  certain  string  so  that 
it  vibrates  100  times  a  second.     If  2000  g.  be  applied,  what 
will  the  pitch  be  ? 

225.  A  certain  string,  1  m.  long,  vibrates  512  times  a  sec- 
ond.    If  its  length  is  reduced  to  250  cm.,  what  will  the  pitch 
be? 

226.  A  force  of  1,000,000  dynes  suffices  to  give  a  certain 
wire  a  pitch  of  100  vibrations  per  second.     The  diameter  of 
the  wire  is  0.02  cm.     What  tension  (in  dynes)  must  be  applied 
to  give  the  same  pitch  to  a  wire  of  the  same  material  and  same 
length,  but  the  diameter  of  which  is  0.1  cm.  ? 

227.  Two  strings  of  the  same  material  are  mounted  side  by 
side  upon  a  sonometer.     One  is  stretched  by  means  of  a  key 
until  its  pitch  is  512  S.  V.     The  other  is  stretched  by  weights 
to  the   same  pitch.     The  weight  required  is  5000  g.      The 
length  of  the  latter  string  is  twice  as  great  and  its  cross-sec- 
tion double  that  of  the  string  stretched  with  the  key.     Find 
the  force  in  dynes  applied  by  means  of  the  key. 

CHAPTER   XXXVIII 

228.  How  long  an  air  column  will  be  in  resonance  with  a 
fork  which  has  a  pitch  of  640  single  vibrations  per  second  ? 
(See  Art.  327.) 

229.  In  the  resonator  depicted  in  Fig.  333,  in  which  direc- 
tion must  the  sliding  part  be  moved  to  make  the  resonator 
respond  to  tones  of  higher  pitch  ?     Why  ? 

230.  In  a  "slide"  trombone  what  is  the  effect  upon  the 
pitch  when  the  slide  is  drawn  out  ?     Explain. 


28  MECHANICS 

231.  A  performer  will  cause   a   trombone  to  utter  several 
notes  differing  in  pitch  without  moving  the  slide.     How  is  this 
done? 

CHAPTER   XXXIX 

232.  What  evidence  is  there  that  light  is  transmitted  by 
some  medium  other  than  the  air;    an  imponderable  medium 
filling  all  space  ? 

233.  Light  from  a  fixed  star  requires  three  years  to  reach 
the  earth.     What  is  the  distance  of  the  star  (in  kilometers  and 
in  miles)  ? 

234.  Light  falls  upon  a  plane  mirror  as  in  Fig.  342.     If  we 
turn  the  mirror  through  an  angle  of  15°,  by  how  large  an  angle 
will  the  path  of  the  reflected  ray  be  changed  ?     Why  ? 

235.  Draw  a  diagram  similar   to   Fig.  344,  and   add  lines 
showing  the  regions  within  which   the   image  of   the  candle 
would  be  visible  and  those  from  which  it  could  not  be  seen. 

236.  In  Fig.  345  suppose  the  source  of  light  a  to  be  moved 
upwards  from  the  axis  of  the  mirror.     Show  by  a  diagram  the 
displacement  of  b  caused  by  a  given  movement  of  a. 

237.  Would  a  thermometer  placed  with  its  bulb  in  the  real 
image  of  the  candle  (Fig.  347)  tend  to  rise  in  temperature? 
Explain.      Extend   your  reasoning   to   the   case  of   a  virtual 
image. 

238.  Objects  always  appear  in  the  direction  from  which  the 
light  which  enters  the  eye  from  them  comes.     Apply  this  to 
the  bent  appearance  of  a  stick   thrust   obliquely  into  water. 
Give  a  diagram. 

239.  A  diver  submerged  beneath  still  water  looks  obliquely 
towards  the  sun.     Will  its  altitude  appear  less  or  greater  than 
it  really  is  ?     (Diagram.) 

240.  To  spear  a  fish,  seen  obliquely  from  above  the  surface 
of  a  lake,  must  one  aim  beyond  it,  or  in  a  more  nearly  vertical 
direction  ?     (Diagram.) 


MECHANICS  29 

241.  Construct  a  diagram  showing  by  lines  the  region  from 
which   looking   upward    towards   the   surface   of    a    glass   of 
water  the  surface  would  seem  to  be  opaque. 

CHAPTER   XL 

242.  If  we  disperse  the  light  from  a  gas  flame,  or  candle 
flame,  and  obtain  its  spectrum,  to  which  of  the  classes  in  Art. 
352  should  we  expect  it  to  belong  ?     Why  ? 

243.  To  which  class  does  the  spectrum  of  the  crater  of  the 
electric  arc  belong  ?     To  which  class  the  spectrum  of  the  arc 
itself?     (See  Art.  273.) 

244.  Draw  a  diagram  showing  how  you  would  arrange  the 
apparatus  for  Experiment  112. 

245.  Why  do  the  absorption  spectra  of  gases  show  black 
lines,  while  in  passing  light  through  solids  and  liquids  whole 
regions  of  the  spectrum  are  cut  away  by  absorption  ? 

CHAPTER   XLI 

246.  Where  must  the  source  of   light  be  in  order  that  a 
"converging"    lens   may   cause   the    rays    after    passage    to 
diverge  ?     Give  diagram. 

247.  Draw  diagrams  of  two  lenses,  each  of  which  has  one 
convex  and  one  concave  face  (concavo-convex  lenses).     One  of 
these  lenses  is  to  be  convergent ;  the  other  divergent. 

248.  In  order  that  image  and  object  may  be  of  the  same  size, 
what  must  be  their  relative  distances  from  the  lens  ? 

249.  Since  lenses  of  small  aperture  give  as  large  images  as 
lenses  of  great  aperture,  why  is  trouble  and  expense  taken  to 
produce  astronomical  telescopes  of  enormous  aperture  ? 

250.  A   certain   telescope   magnifies   200  diameters.     How 
many  times  would  the  apparent  area  of  a  body  like  the  moon 
be  increased  by  means  of  it  ?     How  far  away  would  the  moon 
seem  to  be  when  viewed  through  such  an  instrument  ? 


30  MECHANICS 

251.  What  is  the  difference  between  spherical  and  chromatic 
aberration  ?     How  may  each  be  counteracted  ? 

CHAPTER   XLII 

252.  Suppose  the  two  rays  of  polarized  light  that  emerge 
from  a  doubly  refracting  prism  (Fig.  378)  to  be  viewed  through 
a  Nicol  prism.     Describe  the  phenomena. 

253.  A  bit  of  mica  placed  between  "  crossed  "  Nicol  prisms 
restores  light  to  the  field  of  view.     Describe  what  takes  place. 

254.  In  Experiment  121,  why  do  colors  first  show  them- 
selves at  the  top  of  the  film,  and  why  do  they  tend  to  arrange 
themselves  in  horizontal  bands  ? 

CHAPTER   XLIII 

255.  What  purpose  do  the  humors  of  the  eye  serve  ? 

256.  In  a  certain  eye  the  image  of  objects  at  a  considerable 
distance  falls  behind  the  retina.     Is  the  eye  near  or  far  sighted, 
and  what  must  be  the  kind  of  spectacle  lens  to  aid  vision  ? 

257.  An  eye  lacks  all  power  of  accommodation.     Objects  at 
middle  distance  are  in  focus,  but  not  very  near  nor  very  dis- 
tant objects.     What  kind  of  spectacles  would  aid  in  reading, 
and  what  kind  would  improve  distant  vision  ? 

258.  Name  as  many  cases  as  you  can  of  colors  produced  by 
interference. 

259.  Why  is  it  difficult  to  distinguish  bluish  greens  from 
greenish  blues  by  candle  light  ?     Why  cannot  colors  be  distin- 
guished at  all  by  sodium  light  ? 

260.  Of  what  does  the  spectrum  consist  to  a  red-blind  per- 
son ?   to  a  green-blind  person  ?     (Consult  Arts.  287,  388,  389.) 

261.  How  are  contrast  effects  produced  ? 


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the  increasing  strength  of  the  mathematical  teaching  in  our  university  classes.  In  most  of 
the  existing  text-books  it  appears  to  have  been  assumed  that  the  student  possesses  so 
scanty  a  mathematical  knowledge  that  he  cannot  understand  the  natural  language  of 
physics,  i.e.,  the  language  of  the  calculus.  Some  authors,  on  the  other  hand,  have  assumed 
a  degree  of  mathematical  training  such  that  their  work  is  unreadable  for  nearly  all  under- 
graduates. 

The  present  writers  having  had  occasion  to  teach  large  classes,  the  members  of  which 
were  acquainted  with  the  elementary  principles  of  the  calculus,  have  sorely  felt  the  need  of 
a  text-book  adapted  to  their  students.  The  present  work  is  an  attempt  on  their  part  to 
supply  this  want.  It  is  believed  that  in  very  many  institutions  a  similar  condition  of  affairs 
exists,  and  that  there  is  a  demand  for  a  work  of  a  grade  intermediate  between  that  of  the 
existing  elementary  texts  and  the  advanced  manuals  of  physics. 

No  attempt  has  been  made  in  this  work  to  produce  a  complete  manual  or  compendium 
of  experimental  physics.  The  book  is  planned  to  be  used  in  connection  with  illustrated 
lectures,  in  the  course  of  which  the  phenomena  are  demonstrated  and  described.  The 
authors  have  accordingly  confined  themselves  to  a  statement  of  principles,  leaving  the 
lecturer  to  bring  to  notice  the  phenomena  bas,ed  upon  them.  In  stating  these  principles, 
free  use  has  been  made  of  the  calculus,  but  no  demand  has  been  made  upon  the  student 
beyond  that  supplied  by  the  ordinary  elementary  college  courses  on  this  subject. 

Certain  parts  of  physics  contain  real  and  unavoidable  difficulties.  These  have  not  been 
slurred  over,  nor  have  those  portions  of  the  subject  which  contain  them  been  omitted.  It 
has  been  thought  more  serviceable  to  the  student  and  to  the  teacher  who  may  have  occa- 
sion to  use  the  book  to  face  such  difficulties  frankly,  reducing  the  statements  involving 
them  to  the  simplest  form  which  is  compatible  with  accuracy. 

In  a  word,  the  Elements  of  Physics  is  a  book  which  has  been  written  for  use  in  such 
institutions  as  give  their  undergraduates  a  reasonably  good  mathematical  training.  It  is 
intended  for  teachers  who  desire  to  treat  their  subject  as  an  exact  science,  and  who  are 
prepared  to  supplement  the  brief  subject-matter  of  the  text  by  demonstration,  illustration, 
and  discussion  drawn  from  the  fund  of  their  own  knowledge. 


THE    MACMILLAN    COMPANY. 

NEW  YORK:  CHICAGO: 

66  FIFTH  AVENUE.  ROOM  23,   AUDITORIUM. 


EX 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN     INITIAL     FINE     OF    25     CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 

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66    FIFTH   AVENUE,  NEW  YORK. 


71 


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